Recently, we applied Yang's divide-and-conquer (DC) method to the Hartree-Fock (HF) and hybrid density functional theories and assessed its reliability in calculations of bond-alternating polyene chains. In this paper, we investigate the cut-off behaviour of the HF exchange interaction in the DC-HF method by comparing the results of bond-alternating polyene chains with those of more delocalized uniform polyene chains. The cut-off error of the uniform chain is much larger than that of the bond-alternating chain because of the delocalized electronic structure of the uniform polyene chain. We also estimate the exponential decay coefficient of the cut-off error in the DC scheme and compare it with that of the real-space one-particle density matrix, which can be represented by the band gap in the insulator limit. It can be concluded that the cut-off derived from the DC-HF method can be reduced to an arbitrary magnitude of error by adopting an appropriate buffer radius corresponding to the band gap.

In this study, the divide-and-conquer (DC) method is extended to configuration-interaction singles, time-dependent density functional, and symmetry-adapted cluster configuration interaction (SACCI) theories for enabling excited-state calculations of large systems. In DC-based excited-state theories, one subsystem is selected as the excitation subsystem and analyzed via excited-state calculations. Test calculations for formaldehyde in water and a conjugated aldehyde demonstrate the high accuracy and effectiveness of these methods. To demonstrate the efficiency of the method, we calculated the π-π* excited state of photoactive yellow protein (PYP). The numerical applications to PYP confirm that the DC-SACCI method significantly accelerates the excited-state calculations while maintaining high accuracy.